I have a 24'x24' cinder block foundation with dirt crawlspace straddling the border between 2 drainage basins. Water flows away from the house on all sides. The house has one support beam down the center directly below the front entry and stairs, and the load-bearing wall holding up the second floor is off-center by about 2 feet. The humidity and mold in the crawlspace are causing health problems, and concerns have been raised about the integrity of the structure in and below the first floor. I want to tear out the floors and fill the crawlspace in with cement to end all of these problems all at once, and serve as heat retention for the radiant floor heating that I plan to install.

I just had a basement contractor come to the house, and he says it's a bad idea, but his reasoning doesn't add up to me. It just sounded like he was trying to talk circles around me to sell me vinyl encapsulation with a larger profit margin. What he said was that water would fill up into the cinder blocks and cause problems, but wouldn't specifically say what problems. It seems to me that vinyl encapsulation would be no different because it seals against the cinder blocks just the same as the vapor barrier in a slab. Also, it seems irrelevant considering the cement would be the new floor, so if the water table were to rise high enough for it come over the floor, we'd have problems anyway. Furthermore, with the house straddling two drainage basins, I wouldn't expect water to come up in the cinder blocks at all. He even mentioned that I'd need a sump pump the prevent water problems with a slab, but wouldn't talk to me about it when I asked.

If it's not a terrible risk, I'm determined to have a slab poured. I grew up on a slab and loved the solid feeling under my feet, and we never had to worry about mold, termites, nor rot. Since nobody here will make a profit depending on what I choose, I'm hoping somebody can explain why a slab might be a bad idea without trying to sell me something else, or even better, tell me that the contractor is full of it and I have nothing to worry about.

Your plan makes no since to me.
In order to do what your suggesting the whole house would have to be torn down.
The crawl space would have to be back filled in layers and compacted, a vaper barrier, a layer of foam then pore a slab. Then a whole new house built.
With the house in the way there's no way to do any of that.
There's lots of things that can be done to get rid of the moisture or humity in a crawl space.
Starting outside you need gutters, may need a french drain, waterproofing the outside of the foundation down to the footing, making sure the grade runs away from the foundation, no mulch piled up againt the foundation, no flower beds forming a pond near the foundtion.
Back filling any low spots in the crawl space.
Adding a sump pump.
Foundation vents, 6 mil. plastic as a vaper barrier on the ground under the house.
If your floor joist and subfloor are already molded or have fungus on them any exterminator can spray them with boric acid to kill it and prevent it from coming back.
Running a dehumidifyer in the crawl space.

And the theory of no termites if you have a slab is not even close to being true. All slabs crack when curing. Just one crack is more then enough to let then in. But with a slab they could be getting into the inside walls where no one would know until it's to late.

Sometimes people decide things based on "instinct".
They may be right, but I'd rather give a reason based on consensus or good practice or logic or physics or sumpin'. Figuring out why your instincts are telling you something is not so easy.

You could search "building science" and building code sites to see what they usually recommend, and see what recommendations are "conspicuous by their absence".
Good answers for you may depend on your local climate and your local geology.

You could make having a slab a non-negotiable constraint for this project and have several contractors quote a price. Depending on the quotes it might be worth it to ask a civil engineer for a consult on this.

The thermal inertia and thermal conductivity of your slab would be constant, but the summer/winter ground temperature would change the performance of your radiant system unless the slab is insulated from the ground.

It could be that your contractor was trying to save you from a huge and costly mistake on your part.

Filling in the crawl space with cement could be done but is frankly ridiculous.

Depending upon where you live and if your wet crawl space problem is one of condensation because of a lack of proper venting or high ground water, creating a non-vented crawl space is probably the right thing to do.

Some times keeping a crawspace dry is imposible. We have houses built on the river flats with high water table and crawl spaces that have 6" of mud in them and no possibility of staying ahead of it even with a sump pump. The fix is to convert to slab on grade. It's not easy, it's not cheap and it requires people to move out of the house for some time.
You remove floor sheet and on the out side walls and barring wall, remove the sill plate between floor joists and fill the voids with block to hold up the wall and then remove floor joists and fill in the missing block. 2" foam against the inside of the foundation as deep as you can and 3 1/2" from the top. Fill with sand , re- install sewer lines, compact and cover with poly and pore concrete. If interior walls sag but stay in place cut the bottom foot away and replace that later. A new perimiter drain on the outside dose not have to be as deep as with a crawl space but still important to remove the water.
I have seen this done twice and both were home owners as contractors were just to expensive.
This would be my last choice after looking very hard at every other solution.